Symmetry analysis for time-fractional convection-diffusion equation

TL;DR

This paper applies Lie symmetry analysis to the time-fractional convection-diffusion equation, deriving symmetries, reducing it to fractional ODEs, and obtaining explicit group-invariant solutions.

Contribution

It introduces symmetry analysis to fractional PDEs, providing new reductions and explicit solutions for the time-fractional convection-diffusion equation.

Findings

Symmetries identified in eight cases.

Reduction to fractional ordinary differential equations.

Explicit group-invariant solutions obtained.

Abstract

The time-fractional convection-diffusion equation is performed by Lie symmetry analysis method which involves the Riemann-Liouville time-fractional derivative of the order $\alpha\in(0,2)$. In eight cases, the symmetries are obtained and similarity reductions of the equation are deduced by means of symmetry. It is shown that the fractional equation can be reduced into fractional ordinary differential equations. Some group invariant solutions in explicit form are obtained in some cases.